That's not just a pretty picture above. My friends, say hello to the
1,318 highly interconnected transnational companies (with a core of 147
"super-entities") that rule the world, as visualized by scientists
at the Swiss Federal Insitute of Technology:

From Orbis 2007, a database listing 37 million companies and investors
worldwide, they pulled out all 43,060 TNCs and the share ownerships
linking them. Then they constructed a model of which companies controlled
others through shareholding networks, coupled with each company's operating
revenues, to map the structure of economic power.

The work, to be published in PloS One, revealed a core of 1318
companies with interlocking ownerships (see image). Each of the 1318
had ties to two or more other companies, and on average they were connected
to 20. What's more, although they represented 20 per cent of global
operating revenues, the 1318 appeared to collectively own through their
shares the majority of the world's large blue chip and manufacturing
firms - the "real" economy - representing a further 60 per
cent of global revenues.

When the team further untangled the web of ownership, it found
much of it tracked back to a "super-entity" of 147 even more
tightly knit companies - all of their ownership was held by other members
of the super-entity - that controlled 40 per cent of the total wealth
in the network. "In effect, less than 1 per cent of the companies
were able to control 40 per cent of the entire network," says Glattfelder.
Most were financial institutions. The top 20 included Barclays Bank,
JPMorgan Chase & Co, and The Goldman Sachs Group.

I don't like rich people owning the means of production, but I don't think that's what's going on here.

It depends on what it means for a company to "own" another. I noticed that one of the top companies listed in the study is Vanguard. They are a mutual-fund manager, and specialize in low-fee index funds. Vanguard MANAGES the money of its customers: you give it a pile of your money (usually your retirement money), and they will use it to buy shares in companies. If those companies pay dividends, Vanguard's customers get some of those dividends. If those companies' shares increase in value, Vanguards' customers have more money (on paper).

I don't think that Vanguard has a lot of its own money invested in owning shares of those companies. It's using the customers' money. And that's a good thing, it's exactly what the customers what Vanguard to do!

Since most of the top companies in this list are banks and mutual-fund managers, I suspect what you're seeing here is that a lot of middle-class people are putting their retirement money into mutual funds, and thus collectively own a lot of the world's biggest companies.

It is not accurate to say that the mutual-fund companies actually own the shares of the stocks in their funds. They are investing their customers' money.

Of course, many mutual-fund companies have high fees, and otherwise are greedy and don't play nice, but that's another story.